FIA NLS Models: Biomass Growth vs. Biomass
JAH
2023-04-26
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(tau\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine if including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) is warranted:
model 1: simple tau model \(G = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: tau-alpha model \(G = (1 + (yr-1990)* \tau/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot-based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6822 6736.7
## 2 6821 7534.1 1 -797.33 -721.87 1
## model AIC
## 1 1 27051.87
## 2 2 27817.31##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A *
## B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.2671 0.1775 1.505 0.132
## A 3.2804 0.1160 28.291 <2e-16 ***
## k 6.7587 0.6502 10.394 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9937 on 6822 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.845e-06
## (52 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6822 6736.7
## 2 6821 6727.4 1 9.3448 9.4748 0.002091 **
## 3 6821 6726.7 0 0.0000
## 4 6820 6726.7 1 0.0597 0.0605 0.805680
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 27051.87
## 2 1a 27044.40
## 3 1b 27043.74
## 4 1c 27045.68##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (A *
## B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.25633 0.17692 1.449 0.147
## A 3.58695 0.19865 18.056 < 2e-16 ***
## k 6.67287 0.99212 6.726 1.89e-11 ***
## s 0.65608 0.09614 6.824 9.59e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9931 on 6821 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.378e-06
## (52 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.## Warning: Removed 17 rows containing missing values (`geom_point()`).## Warning: Removed 1038 rows containing missing values (`geom_line()`).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18911 20242
## 2 18910 19105 1 1137.5 1125.9 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70366.34
## 2 2 69274.47##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.42620 0.18105 7.877 3.52e-15 ***
## alpha -0.80627 0.02203 -36.596 < 2e-16 ***
## A 2.44488 0.06875 35.560 < 2e-16 ***
## k 10.00577 0.45256 22.109 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.005 on 18910 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.666e-07
## (3801 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18910 19105
## 2 18909 18935 1 170.352 170.122 < 2.2e-16 ***
## 3 18909 18950 0 0.000
## 4 18908 18933 1 17.327 17.304 3.199e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 69274.47
## 2 2a 69107.06
## 3 2b 69122.31
## 4 2c 69107.01##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.39139 0.17819 7.809 6.08e-15 ***
## alpha 0.79883 0.02187 36.521 < 2e-16 ***
## A 2.78688 0.14055 19.828 < 2e-16 ***
## k 24.81949 2.81959 8.803 < 2e-16 ***
## p 0.19009 0.03300 5.760 8.54e-09 ***
## s 0.84678 0.09699 8.731 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.001 on 18908 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.603e-06
## (3801 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1926 rows containing missing values (`geom_point()`).## Warning: Removed 1031 rows containing missing values (`geom_line()`).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7266 10676
## 2 7265 10233 1 442.85 314.42 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 32681.15
## 2 2 32375.18##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.80333 0.12655 -6.348 2.31e-10 ***
## alpha -0.75378 0.03983 -18.923 < 2e-16 ***
## A 5.20258 0.17244 30.171 < 2e-16 ***
## k 14.06087 1.58685 8.861 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.187 on 7265 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 5.702e-06
## (64 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7265 10233
## 2 7264 10148 1 84.098 60.195 9.767e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 32375.18
## 2 2a 32317.19
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.86646 0.12260 -7.067 1.73e-12 ***
## alpha 0.74899 0.03917 19.122 < 2e-16 ***
## A 7.52676 0.76898 9.788 < 2e-16 ***
## k 202.76459 69.18211 2.931 0.00339 **
## p 0.38169 0.02784 13.708 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.182 on 7264 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 9.007e-06
## (64 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 32 rows containing missing values (`geom_point()`).## Warning: Removed 1036 rows containing missing values (`geom_line()`).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4839 6092.2
## 2 4838 5805.1 1 287.09 239.26 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 20152.37
## 2 2 19920.64##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.11848 0.23118 0.512 0.608
## alpha -0.77706 0.04598 -16.900 <2e-16 ***
## A 4.21858 0.19827 21.277 <2e-16 ***
## k 18.54761 1.56451 11.855 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.095 on 4838 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.671e-06
## (1003 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4838 5805.1
## 2 4837 5690.5 1 114.64 97.441 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 19920.64
## 2 2a 19826.07
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.01938 0.22049 0.088 0.93
## alpha 0.75820 0.04557 16.637 < 2e-16 ***
## A 6.20355 0.50936 12.179 < 2e-16 ***
## k 129.93261 26.49360 4.904 9.68e-07 ***
## p 0.24892 0.01539 16.178 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.085 on 4837 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 4.186e-06
## (1003 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 489 rows containing missing values (`geom_point()`).## Warning: Removed 1053 rows containing missing values (`geom_line()`).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8742 11815
## 2 8741 11535 1 280.04 212.21 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 36909.11
## 2 2 36701.34##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.77933 0.11789 -6.611 4.05e-11 ***
## alpha -0.66734 0.04291 -15.550 < 2e-16 ***
## A 4.87070 0.16409 29.683 < 2e-16 ***
## k 27.85094 2.46399 11.303 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.149 on 8741 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.35e-06
## (1265 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## singular gradient
## model AIC
## 1 2 36701.34
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.77933 0.11789 -6.611 4.05e-11 ***
## alpha -0.66734 0.04291 -15.550 < 2e-16 ***
## A 4.87070 0.16409 29.683 < 2e-16 ***
## k 27.85094 2.46399 11.303 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.149 on 8741 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.35e-06
## (1265 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 620 rows containing missing values (`geom_point()`).## Warning: Removed 1002 rows containing missing values (`geom_line()`).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13233 32413
## 2 13232 29231 1 3182.2 1440.5 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 69085.33
## 2 2 67719.56##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.14896 0.16799 6.839 8.30e-12 ***
## alpha -0.86934 0.02066 -42.070 < 2e-16 ***
## A 4.23734 0.11547 36.696 < 2e-16 ***
## k 1.13765 0.15945 7.135 1.02e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.486 on 13232 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.899e-06
## (281 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13232 29231
## 2 13231 29135 1 96.228 43.7 3.974e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 67719.56
## 2 2a 67677.92
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.09703 0.16521 6.640 3.25e-11 ***
## alpha 0.86928 0.02053 42.333 < 2e-16 ***
## A 4.39923 0.12578 34.975 < 2e-16 ***
## k 7.58697 2.23586 3.393 0.000693 ***
## p 0.53014 0.05089 10.418 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.484 on 13231 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.544e-06
## (281 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 143 rows containing missing values (`geom_point()`).## Warning: Removed 1017 rows containing missing values (`geom_line()`).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13303 36087
## 2 13302 32461 1 3626.1 1485.9 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 69162.02
## 2 2 67754.96##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.83918 0.16820 4.989 6.14e-07 ***
## alpha -0.87045 0.02001 -43.494 < 2e-16 ***
## A 4.38516 0.13112 33.445 < 2e-16 ***
## k 5.25719 0.41118 12.786 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.562 on 13302 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 9.137e-06
## (323 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13302 32461
## 2 13301 32152 1 309.141 127.890 < 2.2e-16 ***
## 3 13301 32176 0 0.000
## 4 13300 32151 1 24.408 10.097 0.001489 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 67754.96
## 2 2a 67629.63
## 3 2b 67639.59
## 4 2c 67631.50##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.75079 0.16223 4.628 3.73e-06 ***
## alpha 0.86565 0.01986 43.588 < 2e-16 ***
## A 4.83596 0.15995 30.235 < 2e-16 ***
## k 24.89028 3.99190 6.235 4.65e-10 ***
## p 0.39867 0.02422 16.458 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.555 on 13301 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.41e-06
## (323 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 169 rows containing missing values (`geom_point()`).## Warning: Removed 931 rows containing missing values (`geom_line()`).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1324 3607.2
## 2 1323 3408.5 1 198.66 77.107 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6965.867
## 2 2 6892.697##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.17879 0.83388 1.414 0.15771
## alpha -0.80260 0.08227 -9.756 < 2e-16 ***
## A 3.93904 0.56558 6.965 5.17e-12 ***
## k 4.16920 1.51020 2.761 0.00585 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.605 on 1323 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.236e-06
## (61 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 6892.697
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.17879 0.83388 1.414 0.15771
## alpha -0.80260 0.08227 -9.756 < 2e-16 ***
## A 3.93904 0.56558 6.965 5.17e-12 ***
## k 4.16920 1.51020 2.761 0.00585 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.605 on 1323 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.236e-06
## (61 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91861, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.1726, p-value = 3.011e-05
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 27 rows containing missing values (`geom_point()`).## Warning: Removed 645 rows containing missing values (`geom_line()`).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 77 126.36
## 2 76 117.18 1 9.1869 5.9586 0.01697 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 417.9807
## 2 2 413.9423##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5590 2.0350 -0.275 0.78429
## alpha -0.9121 0.3388 -2.692 0.00874 **
## A 9.3458 4.5294 2.063 0.04249 *
## k 28.8091 14.7620 1.952 0.05467 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.242 on 76 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.5e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 76 117.18
## 2 75 114.38 1 2.79832 1.8349 0.1796
## 3 74 114.22 1 0.15746 0.1020 0.7503
## model AIC
## 1 2 413.9423
## 2 2a 414.0086
## 3 2b NA
## 4 2c 415.8984##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.5590 2.0350 -0.275 0.78429
## alpha -0.9121 0.3388 -2.692 0.00874 **
## A 9.3458 4.5294 2.063 0.04249 *
## k 28.8091 14.7620 1.952 0.05467 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.242 on 76 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.5e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89128, p-value = 5.315e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.28449, p-value = 0.776
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (`geom_point()`).## Warning: Removed 725 rows containing missing values (`geom_line()`).
plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1785 2717.6
## 2 1784 2703.8 1 13.826 9.1224 0.002561 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7661.536
## 2 2 7654.416##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.4846 0.5115 0.947 0.34361
## alpha -0.3806 0.1210 -3.147 0.00168 **
## A 3.2219 0.3152 10.222 < 2e-16 ***
## k 15.3007 3.2666 4.684 3.03e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.231 on 1784 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 4.779e-06
## (507 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1784 2703.8
## 2 1782 2593.8 2 110.03 37.797 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 7654.416
## 2 2a NA
## 3 2b NA
## 4 2c 7584.133##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.2216 0.4513 0.491 0.6234
## alpha 0.2054 0.1148 1.789 0.0738 .
## A 9.9611 18.2443 0.546 0.5851
## k 350.7417 586.1704 0.598 0.5497
## s 2.1843 1.1436 1.910 0.0563 .
## p 0.2280 0.4258 0.535 0.5924
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.206 on 1782 degrees of freedom
##
## Number of iterations to convergence: 25
## Achieved convergence tolerance: 8.153e-06
## (507 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.73045, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.4834, p-value = 8.967e-11
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 254 rows containing missing values (`geom_point()`).## Warning: Removed 1176 rows containing missing values (`geom_line()`).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 670 1600.1
## 2 669 1996.4 1 -396.25 -132.79 1
## model AIC
## 1 1 3143.502
## 2 2 3294.404##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A *
## B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.06116 0.86272 0.071 0.944
## A 2.61726 0.46221 5.662 2.21e-08 ***
## k 0.65106 0.61720 1.055 0.292
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.545 on 670 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.46e-06
## (44 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 670 1600.1
## 2 669 1598.5 1 1.5945 0.6673 0.4143
## model AIC
## 1 1 3143.502
## 2 1a 3144.831
## 3 1b 3144.809
## 4 1c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A *
## B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.06116 0.86272 0.071 0.944
## A 2.61726 0.46221 5.662 2.21e-08 ***
## k 0.65106 0.61720 1.055 0.292
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.545 on 670 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.46e-06
## (44 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91752, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.2822, p-value = 1.276e-07
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 25 rows containing missing values (`geom_point()`).## Warning: Removed 1235 rows containing missing values (`geom_line()`).
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
note: model fit, but fit was funky due to data being sparse
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 212 109.50
## 2 211 105.09 1 4.4098 8.854 0.003266 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 506.5831
## 2 2 499.7454##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.4057 0.8630 -1.629 0.104840
## alpha -0.8581 0.2552 -3.363 0.000917 ***
## A 4.8742 1.6179 3.013 0.002906 **
## k 126.0935 43.2118 2.918 0.003904 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7057 on 211 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 1.9e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 211 105.089
## 2 210 102.361 1 2.7279 5.5964 0.01891 *
## 3 209 99.895 1 2.4666 5.1606 0.02412 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 499.7454
## 2 2a 496.0908
## 3 2b NA
## 4 2c 492.8465##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.45800 0.80966 -1.801 0.073181 .
## alpha 0.86175 0.24671 3.493 0.000583 ***
## A 3.53528 1.11165 3.180 0.001695 **
## k 108.86093 23.64573 4.604 7.2e-06 ***
## s 3.01534 1.38858 2.172 0.031017 *
## p 0.31269 0.09234 3.386 0.000846 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6914 on 209 degrees of freedom
##
## Number of iterations to convergence: 17
## Achieved convergence tolerance: 6.641e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9805, p-value = 0.004507
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.34157, p-value = 0.7327
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (`geom_point()`).## Warning: Removed 1103 rows containing missing values (`geom_line()`).
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in nls(fg_1, data = G_331, start = c(tau = tau.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(tau = tau.start, alpha = alpha.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not foundsummary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 193 173.52
## 2 192 168.70 1 4.8201 5.4858 0.0202 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 665.6359
## 2 2 662.1143##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.8048 1.7052 0.472 0.63747
## alpha -0.6583 0.2567 -2.564 0.01110 *
## A 3.8161 1.2658 3.015 0.00292 **
## k 57.9499 19.0680 3.039 0.00270 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9374 on 192 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.683e-06
## (36 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 192 168.70
## 2 191 160.56 1 8.1352 9.6773 0.002152 **
## 3 190 158.50 1 2.0692 2.4805 0.116929
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 662.1143
## 2 2a 654.4271
## 3 2b NA
## 4 2c 653.8849##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.52731 1.48372 0.355 0.72269
## alpha 0.67320 0.22864 2.944 0.00364 **
## A 3.71061 1.25148 2.965 0.00342 **
## k 85.53537 27.33749 3.129 0.00203 **
## p 0.28897 0.09744 2.966 0.00341 **
## s 2.32866 1.15746 2.012 0.04565 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9133 on 190 degrees of freedom
##
## Number of iterations to convergence: 14
## Achieved convergence tolerance: 6.979e-06
## (36 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91126, p-value = 1.852e-09
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.2715, p-value = 0.2035
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 21 rows containing missing values (`geom_point()`).## Warning: Removed 1120 rows containing missing values (`geom_line()`).
plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 112 82.270
## 2 111 74.205 1 8.065 12.064 0.0007339 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 315.0331
## 2 2 305.1679##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.9428 5.3488 0.363 0.7171
## alpha -0.9852 0.2434 -4.048 9.58e-05 ***
## A 3.2751 2.6546 1.234 0.2199
## k 82.6440 32.5518 2.539 0.0125 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8176 on 111 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.756e-06
## (9 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 111 74.205
## 2 110 74.164 1 0.04076 0.0605 0.8062
## model AIC
## 1 2 305.1679
## 2 2a 307.1047
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.9428 5.3488 0.363 0.7171
## alpha -0.9852 0.2434 -4.048 9.58e-05 ***
## A 3.2751 2.6546 1.234 0.2199
## k 82.6440 32.5518 2.539 0.0125 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8176 on 111 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.756e-06
## (9 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94862, p-value = 0.0002394
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 4 rows containing missing values (`geom_point()`).## Warning: Removed 1241 rows containing missing values (`geom_line()`).
plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6746 5753.1
## 2 6745 5409.4 1 343.7 428.55 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25694.00
## 2 2 25280.27##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.66462 0.19759 3.364 0.000774 ***
## alpha -0.64343 0.02893 -22.243 < 2e-16 ***
## A 3.07739 0.11482 26.801 < 2e-16 ***
## k 2.85208 0.41233 6.917 5.04e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8955 on 6745 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.962e-06
## (23 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6745 5409.4
## 2 6744 5406.1 1 3.3122 4.1319 0.042121 *
## 3 6744 5409.2 0 0.0000
## 4 6743 5402.0 1 7.1869 8.9709 0.002753 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 25280.27
## 2 2a 25278.13
## 3 2b 25281.98
## 4 2c 25275.01##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.65138 0.19644 3.316 0.000918 ***
## alpha 0.64104 0.02888 22.198 < 2e-16 ***
## A 3.03312 0.11388 26.634 < 2e-16 ***
## k 9.63600 2.28136 4.224 2.43e-05 ***
## p 0.44875 0.08007 5.604 2.17e-08 ***
## s 1.77709 0.43212 4.113 3.96e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8951 on 6743 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.728e-06
## (23 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 10 rows containing missing values (`geom_point()`).## Warning: Removed 1108 rows containing missing values (`geom_line()`).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8257 16789
## 2 8256 16419 1 369.5 185.79 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40113.33
## 2 2 39931.50##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.02238 0.16479 -0.136 0.892
## alpha -0.81544 0.05665 -14.395 < 2e-16 ***
## A 4.21394 0.15149 27.817 < 2e-16 ***
## k 7.39990 1.43242 5.166 2.45e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.41 on 8256 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.344e-06
## (55 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 39931.5
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.02238 0.16479 -0.136 0.892
## alpha -0.81544 0.05665 -14.395 < 2e-16 ***
## A 4.21394 0.15149 27.817 < 2e-16 ***
## k 7.39990 1.43242 5.166 2.45e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.41 on 8256 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.344e-06
## (55 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 29 rows containing missing values (`geom_point()`).## Warning: Removed 982 rows containing missing values (`geom_line()`).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 887 1339.4
## 2 886 1293.6 1 45.802 31.369 2.846e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3727.581
## 2 2 3698.615##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.1263 1.5722 1.989 0.0471 *
## alpha -0.9187 0.1511 -6.082 1.77e-09 ***
## A 1.7439 0.3583 4.866 1.34e-06 ***
## k 3.5365 3.1342 1.128 0.2595
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.208 on 886 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 7.383e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 886 1293.6
## 2 885 1298.1 1 -4.4727 -3.0494 1
## model AIC
## 1 2 3698.615
## 2 2a 3703.687
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.1263 1.5722 1.989 0.0471 *
## alpha -0.9187 0.1511 -6.082 1.77e-09 ***
## A 1.7439 0.3583 4.866 1.34e-06 ***
## k 3.5365 3.1342 1.128 0.2595
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.208 on 886 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 7.383e-06
## (6 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94608, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.0441, p-value = 0.04094
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 3 rows containing missing values (`geom_point()`).## Warning: Removed 1175 rows containing missing values (`geom_line()`).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 989 1487.8
## 2 988 1416.7 1 71.015 49.524 3.661e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4215.211
## 2 2 4168.693##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 4.9467 2.5181 1.964 0.049759 *
## alpha -0.7944 0.1046 -7.597 7e-14 ***
## A 1.4589 0.3868 3.772 0.000172 ***
## k 1.4613 0.9078 1.610 0.107771
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.197 on 988 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 8.21e-06
## (14 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 2 4168.693
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 4.9467 2.5181 1.964 0.049759 *
## alpha -0.7944 0.1046 -7.597 7e-14 ***
## A 1.4589 0.3868 3.772 0.000172 ***
## k 1.4613 0.9078 1.610 0.107771
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.197 on 988 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 8.21e-06
## (14 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9557, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.4105, p-value = 6.286e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.## Warning: Removed 6 rows containing missing values (`geom_point()`).## Warning: Removed 1218 rows containing missing values (`geom_line()`).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3147 8417.1
## 2 3146 8013.0 1 404.08 158.65 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 16149.88
## 2 2 15996.91##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.7104 0.2352 -7.271 4.47e-13 ***
## alpha -0.9679 0.0693 -13.967 < 2e-16 ***
## A 12.8005 1.0512 12.177 < 2e-16 ***
## k 128.0294 10.2047 12.546 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.596 on 3146 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.03e-06
## (74 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3146 8013.0
## 2 3145 7895.5 1 117.522 46.813 9.349e-12 ***
## 3 3145 7927.2 0 0.000
## 4 3144 7884.8 1 42.386 16.901 4.038e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 15996.91
## 2 2a 15952.37
## 3 2b 15965.01
## 4 2c 15950.12##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.69947 0.23420 -7.256 4.98e-13 ***
## alpha 0.93948 0.06980 13.459 < 2e-16 ***
## A 11.74044 1.14133 10.287 < 2e-16 ***
## k 171.08730 20.21043 8.465 < 2e-16 ***
## p 0.20420 0.03023 6.755 1.70e-11 ***
## s 1.60173 0.23623 6.780 1.43e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.584 on 3144 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 6.004e-06
## (74 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92456, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.5939, p-value = 4.35e-06
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 38 rows containing missing values (`geom_point()`).## Warning: Removed 126 rows containing missing values (`geom_line()`).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1682 3723.6
## 2 1681 3631.6 1 91.984 42.578 8.964e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7999.216
## 2 2 7959.068##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.7342 0.3391 -5.114 3.52e-07 ***
## alpha -0.7483 0.1059 -7.063 2.37e-12 ***
## A 15.7046 1.8786 8.360 < 2e-16 ***
## k 237.0276 28.7807 8.236 3.55e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.47 on 1681 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 6.485e-06
## (292 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1681 3631.6
## 2 1680 3599.4 1 32.142 15.002 0.0001115 ***
## 3 1680 3620.7 0 0.000
## 4 1679 3591.9 1 28.717 13.424 0.0002562 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 7959.068
## 2 2a 7946.088
## 3 2b 7955.994
## 4 2c 7944.576##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.69541 0.34600 -4.900 1.05e-06 ***
## alpha 0.74116 0.10357 7.156 1.24e-12 ***
## A 13.70695 2.47143 5.546 3.39e-08 ***
## k 225.44963 53.31612 4.229 2.48e-05 ***
## p 0.10497 0.03363 3.121 0.00183 **
## s 1.39890 0.24458 5.720 1.26e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.463 on 1679 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 4.741e-06
## (292 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89641, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.6852, p-value = 0.09195
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 154 rows containing missing values (`geom_point()`).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 363 173.85
## 2 362 154.17 1 19.68 46.209 4.395e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 867.4285
## 2 2 825.4588##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.2781 0.2890 -7.883 3.78e-14 ***
## alpha -0.8248 0.1070 -7.706 1.26e-13 ***
## A 9.7691 1.7843 5.475 8.19e-08 ***
## k 158.4554 37.6226 4.212 3.20e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6526 on 362 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.138e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 362 154.17
## 2 361 153.17 1 1.00231 2.3623 0.1252
## 3 361 153.11 0 0.00000
## 4 360 153.10 1 0.00292 0.0069 0.9341
## model AIC
## 1 2 825.4588
## 2 2a 825.0716
## 3 2b 824.9169
## 4 2c 826.9099##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.2633 0.2924 -7.741 1.00e-13 ***
## alpha 0.8207 0.1072 7.655 1.78e-13 ***
## A 46.4898 151.8218 0.306 0.759619
## k 3531.0905 21347.2370 0.165 0.868712
## s 0.6912 0.1784 3.874 0.000127 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6512 on 361 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 2.197e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97183, p-value = 1.539e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 1.2648, p-value = 0.2059
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1183 rows containing missing values (`geom_line()`).
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1732 1567.7
## 2 1731 1472.8 1 94.836 111.46 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4946.994
## 2 2 4840.726##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.76227 0.57791 -1.319 0.187
## alpha -0.70080 0.05633 -12.441 < 2e-16 ***
## A 2.47728 0.38500 6.434 1.60e-10 ***
## k 36.87998 6.05255 6.093 1.36e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9224 on 1731 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.598e-06
## (21 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1731 1472.8
## 2 1730 1444.8 1 28.005 33.533 8.306e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 4840.726
## 2 2a 4809.418
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.52155 0.64055 -0.814 0.41563
## alpha 0.71336 0.05463 13.058 < 2e-16 ***
## A 5.86779 2.73742 2.144 0.03221 *
## k 480.19280 344.85521 1.392 0.16397
## p 0.12897 0.04919 2.622 0.00883 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9139 on 1730 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.581e-07
## (21 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.85285, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.0675, p-value = 1.299e-09
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 7 rows containing missing values (`geom_point()`).## Warning: Removed 1091 rows containing missing values (`geom_line()`).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2513 2864.1
## 2 2512 2605.7 1 258.36 249.07 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8728.807
## 2 2 8492.947##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.83940 0.43557 -1.927 0.0541 .
## alpha -0.90696 0.04938 -18.366 < 2e-16 ***
## A 4.67956 0.57797 8.097 8.72e-16 ***
## k 63.69769 7.00966 9.087 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.018 on 2512 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 5.412e-06
## (96 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2512 2605.7
## 2 2511 2493.1 1 112.67 113.49 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 8492.947
## 2 2a 8383.730
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.90399 0.40784 -2.216 0.02675 *
## alpha 0.88994 0.04846 18.364 < 2e-16 ***
## A 15.03808 5.94947 2.528 0.01154 *
## k 778.59152 400.54032 1.944 0.05202 .
## p 0.07483 0.02517 2.972 0.00298 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9964 on 2511 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.226e-06
## (96 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90403, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.8038, p-value = 1.019e-11
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 54 rows containing missing values (`geom_point()`).## Warning: Removed 1001 rows containing missing values (`geom_line()`).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1691 2122.4
## 2 1690 1851.2 1 271.16 247.54 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6712.211
## 2 2 6482.658##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.57735 0.57364 -1.006 0.314
## alpha -0.94904 0.05263 -18.031 < 2e-16 ***
## A 5.53729 0.80951 6.840 1.1e-11 ***
## k 44.22062 4.89719 9.030 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.047 on 1690 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 9.13e-06
## (59 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1690 1851.2
## 2 1689 1754.2 1 97.099 93.493 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 6482.658
## 2 2a 6393.391
## 3 2b NA
## 4 2c NA##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.64166 0.54008 -1.188 0.234968
## alpha 0.93153 0.05060 18.408 < 2e-16 ***
## A 13.16763 3.39124 3.883 0.000107 ***
## k 464.03966 162.05800 2.863 0.004243 **
## p 0.11466 0.02073 5.532 3.67e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.019 on 1689 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 9.076e-06
## (59 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93181, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.6928, p-value = 2.695e-06
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 26 rows containing missing values (`geom_point()`).## Warning: Removed 925 rows containing missing values (`geom_line()`).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 355 353.04
## 2 354 327.07 1 25.967 28.104 2.028e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1090.416
## 2 2 1065.066##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.06351 1.23785 0.051 0.959111
## alpha -0.80377 0.13376 -6.009 4.64e-09 ***
## A 2.35196 0.61035 3.853 0.000138 ***
## k 29.82188 9.39819 3.173 0.001640 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9612 on 354 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.666e-06
## (101 observations deleted due to missingness)summary
- simple model: fits
- alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 + alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 354 327.07
## 2 353 327.04 1 0.03769 0.0407 0.8403
## 3 353 327.03 0 0.00000
## 4 352 326.23 1 0.80050 0.8637 0.3533
## model AIC
## 1 2 1065.066
## 2 2a 1067.025
## 3 2b 1067.014
## 4 2c 1068.136##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 +
## alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.06351 1.23785 0.051 0.959111
## alpha -0.80377 0.13376 -6.009 4.64e-09 ***
## A 2.35196 0.61035 3.853 0.000138 ***
## k 29.82188 9.39819 3.173 0.001640 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9612 on 354 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 9.666e-06
## (101 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.83083, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.0095, p-value = 0.002616
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 40 rows containing missing values (`geom_point()`).## Warning: Removed 1264 rows containing missing values (`geom_line()`).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 1b |
| 212 | Laurentian Mixed Forest | 2c |
| 221 | Eastern Broadleaf Forest | 2a |
| 222 | Midwest Broadleaf Forest | 2a |
| 223 | Central Interior Broadleaf Forest | 2 |
| 231 | Southeastern Mixed Forest | 2a |
| 232 | Outer Coastal Plain Mixed Forest | 2a |
| 234 | Lower Mississippi Riverine Forest | 2 |
| 242 | Pacific Lowland Mixed Forest | 2 |
| 251 | Prairie Parkland (Temperate) | 2c |
| 255 | Prairie Parkland (Subtropical) | 1 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | 2c |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | 2c |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | 2 |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2c |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2 |
| M223 | Ozark Broadleaf Forest Meadow | 2 |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 2c |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2c |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2b |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2a |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a |
| M334 | Black Hills Coniferous Forest | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6877 | 2876 | 0.2563300 | 0.0313012 | -0.0904912 | 0.6031512 | NA | NA | NA | NA | 3.586948 | 3.1975283 | 3.976368 | 6.6728734 | 4.728000e+00 | 8.617747 |
| 212 | Laurentian Mixed Forest | east | 22715 | 9499 | 1.3913875 | 0.0317501 | 1.0421278 | 1.7406472 | 0.7988278 | 0.0004784 | 0.7559542 | 0.8417013 | 2.786876 | 2.5113784 | 3.062373 | 24.8194914 | 1.929284e+01 | 30.346147 |
| 221 | Eastern Broadleaf Forest | east | 7333 | 3571 | -0.8664562 | 0.0150309 | -1.1067890 | -0.6261234 | 0.7489933 | 0.0015342 | 0.6722112 | 0.8257755 | 7.526758 | 6.0193286 | 9.034187 | 202.7645861 | 6.714754e+01 | 338.381632 |
| 222 | Midwest Broadleaf Forest | east | 5845 | 2589 | 0.0193829 | 0.0486172 | -0.4128837 | 0.4516496 | 0.7582044 | 0.0020771 | 0.6688572 | 0.8475515 | 6.203547 | 5.2049709 | 7.202122 | 129.9326131 | 7.799312e+01 | 181.872103 |
| 223 | Central Interior Broadleaf Forest | east | 10010 | 3864 | -0.7793322 | 0.0138981 | -1.0104251 | -0.5482392 | -0.6673416 | 0.0018417 | -0.7514642 | -0.5832189 | 4.870700 | 4.5490425 | 5.192357 | 27.8509429 | 2.302094e+01 | 32.680950 |
| 231 | Southeastern Mixed Forest | east | 13517 | 6193 | 1.0970279 | 0.0272942 | 0.7731933 | 1.4208625 | 0.8692755 | 0.0004217 | 0.8290255 | 0.9095256 | 4.399229 | 4.1526809 | 4.645777 | 7.5869657 | 3.204365e+00 | 11.969566 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13629 | 6626 | 0.7507905 | 0.0263187 | 0.4327960 | 1.0687850 | 0.8656530 | 0.0003944 | 0.8267250 | 0.9045811 | 4.835960 | 4.5224431 | 5.149478 | 24.8902847 | 1.706559e+01 | 32.714974 |
| 234 | Lower Mississippi Riverine Forest | east | 1388 | 778 | 1.1787939 | 0.6953602 | -0.4570826 | 2.8146704 | -0.8025954 | 0.0067680 | -0.9639845 | -0.6412062 | 3.939045 | 2.8295221 | 5.048568 | 4.1692019 | 1.206553e+00 | 7.131851 |
| 242 | Pacific Lowland Mixed Forest | pacific | 83 | 83 | -0.5590174 | 4.1412960 | -4.6121059 | 3.4940711 | -0.9120660 | 0.1148026 | -1.5868951 | -0.2372368 | 9.345847 | 0.3247658 | 18.366928 | 28.8091141 | -5.919517e-01 | 58.210180 |
| 251 | Prairie Parkland (Temperate) | east | 2295 | 906 | 0.2216359 | 0.2037144 | -0.6635898 | 1.1068616 | 0.2054172 | 0.0131859 | -0.0197979 | 0.4306323 | 9.961071 | -25.8213578 | 45.743499 | 350.7416996 | -7.989121e+02 | 1500.395489 |
| 255 | Prairie Parkland (Subtropical) | east | 717 | 319 | 0.0611564 | 0.7442863 | -1.6328044 | 1.7551171 | NA | NA | NA | NA | 2.617256 | 1.7096987 | 3.524814 | 0.6510643 | -5.608122e-01 | 1.862941 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 25 | 25 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 163 | 161 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | -1.4580008 | 0.6555427 | -3.0541398 | 0.1381382 | 0.8617501 | 0.0608675 | 0.3753845 | 1.3481157 | 3.535280 | 1.3438044 | 5.726756 | 108.8609268 | 6.224623e+01 | 155.475628 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | 0.5273135 | 2.2014395 | -2.3993756 | 3.4540026 | 0.6732000 | 0.0522762 | 0.2222013 | 1.1241987 | 3.710606 | 1.2420309 | 6.179182 | 85.5353659 | 3.161140e+01 | 139.459329 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | 1.9428128 | 28.6091636 | -8.6560993 | 12.5417248 | -0.9851536 | 0.0592234 | -1.4673851 | -0.5029222 | 3.275141 | -1.9851322 | 8.535414 | 82.6440257 | 1.814043e+01 | 147.147617 |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6772 | 3006 | 0.6513800 | 0.0385875 | 0.2663014 | 1.0364587 | 0.6410399 | 0.0008339 | 0.5844300 | 0.6976499 | 3.033122 | 2.8098797 | 3.256365 | 9.6360019 | 5.163818e+00 | 14.108185 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8315 | 3810 | -0.0223837 | 0.0271568 | -0.3454200 | 0.3006526 | -0.8154360 | 0.0032089 | -0.9264781 | -0.7043938 | 4.213936 | 3.9169781 | 4.510893 | 7.3998973 | 4.591995e+00 | 10.207799 |
| M223 | Ozark Broadleaf Forest Meadow | east | 896 | 349 | 3.1263420 | 2.4716768 | 0.0407563 | 6.2119277 | -0.9186634 | 0.0228168 | -1.2151257 | -0.6222011 | 1.743872 | 1.0405732 | 2.447170 | 3.5364747 | -2.614832e+00 | 9.687782 |
| M231 | Ouachita Mixed Forest | east | 1006 | 495 | 4.9466961 | 6.3409406 | 0.0052133 | 9.8881789 | -0.7943535 | 0.0109322 | -0.9995334 | -0.5891735 | 1.458943 | 0.6999145 | 2.217972 | 1.4612679 | -3.200901e-01 | 3.242626 |
| M242 | Cascade Mixed Forest | pacific | 3224 | 3207 | -1.6994737 | 0.0548502 | -2.1586764 | -1.2402711 | 0.9394760 | 0.0048721 | 0.8026171 | 1.0763350 | 11.740440 | 9.5026144 | 13.978265 | 171.0873034 | 1.314603e+02 | 210.714270 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1977 | 1807 | -1.6954110 | 0.1197185 | -2.3740549 | -1.0167672 | 0.7411577 | 0.0107271 | 0.5380143 | 0.9443011 | 13.706949 | 8.8595352 | 18.554362 | 225.4496302 | 1.208766e+02 | 330.022689 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -2.2633319 | 0.0854902 | -2.8383280 | -1.6883359 | 0.8206775 | 0.0114930 | 0.6098518 | 1.0315032 | 46.489850 | -252.0764727 | 345.056172 | 3531.0904921 | -3.844947e+04 | 45511.650585 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1756 | 1756 | -0.5215501 | 0.4103002 | -1.7778776 | 0.7347775 | 0.7133635 | 0.0029846 | 0.6062123 | 0.8205148 | 5.867793 | 0.4987919 | 11.236793 | 480.1928029 | -1.961842e+02 | 1156.569814 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2612 | 2602 | -0.9039865 | 0.1663372 | -1.7037327 | -0.1042403 | 0.8899359 | 0.0023485 | 0.7949068 | 0.9849650 | 15.038079 | 3.3717145 | 26.704444 | 778.5915153 | -6.831681e+00 | 1564.014712 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1753 | 1742 | -0.6416558 | 0.2916837 | -1.7009473 | 0.4176356 | 0.9315265 | 0.0025607 | 0.8322748 | 1.0307783 | 13.167626 | 6.5161470 | 19.819105 | 464.0396645 | 1.461840e+02 | 781.895283 |
| M334 | Black Hills Coniferous Forest | interior west | 459 | 181 | 0.0635085 | 1.5322693 | -2.3709535 | 2.4979705 | -0.8037708 | 0.0178929 | -1.0668432 | -0.5406984 | 2.351961 | 1.1515878 | 3.552334 | 29.8218782 | 1.133858e+01 | 48.305176 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
parameter variance co-variance
## png
## 2plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot alpha (biomass growth compensation effect)
plot A (asymptote of forest biomass growth in Mg/ha/yr)
## Warning: Removed 12 rows containing missing values (`geom_point()`).
plot k (stand biomass at half biomss G in Mg/ha)
## Warning: Removed 12 rows containing missing values (`geom_point()`).
Caclulations - weighted averages
tau (stand biomass productivity trend in % 2000-2021)
## region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1 entire US 0.21477279 0.06490419 0.34198500
## 2 pacific -0.14778107 0.01712126 -0.11422340
## 3 east 0.45260667 0.05268286 0.55586508
## 4 interior west -0.09005281 0.03382207 -0.02376156
## 95 % CI, lower
## 1 0.08756058
## 2 -0.18133874
## 3 0.34934826
## 4 -0.15634406alpha (biomass growth compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.48701599 0.010032499 0.50667969
## 2 pacific 0.07382771 0.005060543 0.08374637
## 3 east 0.31824548 0.007951336 0.33383010
## 4 interior west 0.09494281 0.003437762 0.10168082
## 95 % CI, lower
## 1 0.46735229
## 2 0.06390905
## 3 0.30266086
## 4 0.08820479A (asymptote of forest biomass growth in Mg/ha/yr)
## region weighted.A
## 1 entire US 6.076233
## 2 pacific 11.962096
## 3 east 4.389088
## 4 interior west 11.887101K (stand biomass at half biomass G in Mg/ha)
## region weighted.k
## 1 entire US 138.06413
## 2 pacific 181.42260
## 3 east 44.83991
## 4 interior west 652.58823